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## Introduction

A monomial is an algebraic expression containing a single term.  A polynomial is an algebraic expression containing multiple terms.  Below are some examples of monomials and polynomials.

A polynomial with two terms is called a binomial and one with three terms is a trinomial.

Most new topics in mathematics are introduced with the easiest problems first followed by the more complicated problems later.  The problems in this lesson involve multiplying two expressions, one of them being a monomial.  It is important that you completely understand this beginning material before moving on to more complicated polynomial multiplication.

## Lesson

This is the first of several lessons on the topic of multiplying polynomials.  Since a polynomial is comprised of several individual terms, the distributive property is used to do the multiplication.

In the problem to the left, the 6 is distributed to each term in the trinomial 2a2 + 5a + 3.  Once the 6 is distributed to each term in the trinomial, the multiplication that follows is actually rather easy.

In the problem to the right, the term that is distributed is the 8b.  The multiplication here is slightly more difficult because you must multiply the 8 times the number in each term and the b times the variable in each term.

This third problem is the first problem in this lesson that contains a minus sign in the polynomial.  The problem can be worked in much the same way as the first two problems in this lesson.  Notice that the minus sign remains in the same position throughout the work and in the answer.

When the negative sign is found in the monomial, it must also be distributed to each term of the polynomial.  Two examples of this are given so that you can get a good idea of exactly how to simplify any problem where a negative monomial is multiplied by a polynomial.

## Try It

1)  5(2m2 – 3m + 6)

2)  2n2(-4n3 + 9n2 + 3n – 10)

3)  3p(-2p5 – p4 + - 2p3 + 11p2 – 3p)

4)  -5(2q3+ 3q2 – 11q + 5)

5)  -8r2(14 + 4r2 – 3r3 – 5r)

1)  10m2 – 15m + 30

2)  -8n5 + 18n4 + 6n3 – 20n2

3)  -6p6 – 3p5 + - 6p4 + 33p3 – 9p2

4)  -10q3 – 15q2 + 55q – 25

5)  -112r2 – 32r4 + 24r5 + 40r3 , which equals 24r5 – 32r4 + 40r3 – 112r2 in standard form.

Didn't find what you were looking for in this lesson?  More information on polynomials can be found at the following places:

Resource Page

Related Lessons

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